WASHINGTON — President Obama tenaciously defended Ambassador Susan Rice on Wednesday, using his first postelection news conference to label as “outrageous” any Republican charges that the diplomat misled the American public after the attack on a US Consulate in Libya on Sept. 11.

Much of the press conference, his first in five months, centered on coming negotiations with Congress to avoid a fiscal maelstrom of mandated tax increases and budget cuts at the end of the year. Obama also renewed a call for immigration reform – and said conversations were already underway with congressional leaders — but said legislation addressing climate change would be much more difficult.

The 52-minute conference displayed an assertive, confident president following his resounding reelection win over Mitt Romney just eight days earlier and forecast the types of battles that would be fought with Congress over the next few weeks. But the most poignant and animated part was the president’s support of Rice, who is in contention along with Senator John Kerry to replace Hillary Clinton as secretary of state.

“If Senator [John] McCain and Senator [Lindsey] Graham, and others want to go after somebody?” Obama said, naming the two most aggressive critics of Rice. “They should go after me.

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“When they go after the UN ambassador, apparently because they think she’s an easy target, then they’ve got a problem with me. And should I choose, if I think that she would be the best person to serve America, in the capacity of the State Department, then I will nominate her.’’

Graham fired back, just as the conference ended, with a statement saying the president failed before, during, and after the attack. Later, he told reporters he would never support Rice if she were nominated for secretary of state. “He’ll have one hell of a fight and that will be of his choosing,’’ the South Carolina Republican said of Obama. “I don’t want to fight, but I’ve got a conscience, too.’’

Republicans have criticized the administration’s shifting explanation of the attack in Libya that killed Ambassador Christopher Stevens and three other Americans. They have been calling for expansive congressional hearings on what went wrong, whether the administration failed to respond properly, and whether any coverup ensued.

Rice has been a focal point for the criticism, with Republicans pointing to her initial response several days after the attack when she said it appeared to be a spontaneous reaction inspired by an anti-Muslim video. That turned out to be false, with most evidence pointing to a planned terrorist attack, but administration officials have said Rice was summing up the intelligence information known at the time.

Republican senators — led by McCain, Graham, and Senator Kelly Ayotte of New Hampshire — called Wednesday for a special investigative committee.

“This president and this administration has either been guilty of colossal incompetence or engaged in a coverup,” McCain said on the Senate floor.

Obama’s strong defense of Rice could indicate he is willing to fight over her nomination if he determines she’s the best candidate to replace Clinton, who said she is ready to step aside as Obama begins his second term.

The White House is now confronted with the decision over whether to expend political capital on pushing for Rice or whether they would try to nominate Kerry, who would likely have a much easier path to confirmation.

“John Kerry is a very qualified man,” Graham volunteered. “If the president thought John Kerry could serve his administration and the country I would be very inclined to support him.”

Kerry, who has also been floated as a candidate for defense secretary, urged colleagues to wait for Clinton to complete her investigation on Benghazi, and he praised Rice as “a remarkable public servant.”

“She’s an enormously capable person who has represented us at the United Nations with strength and character,” Kerry told the Globe. “We all want to know what happened in Benghazi, and I know that on a deeply personal level no one wants those answers more than President Obama because he sent our fallen Americans overseas and he greeted their caskets when they came home.”

Several questions and followup attempts at Obama’s news conference were focused on negotiations to avoid what has been dubbed a fiscal cliff of tax hikes and spending cuts. Obama pledged anew to fight any Republican efforts to extend tax cuts for the wealthy.

Instead, he argued for a two-step process that would have lawmakers first pass a bill that ensures taxes will not rise on the vast majority of Americans and then proceed to the knotty long-term questions over entitlement overhaul and broad changes to the tax code.

If the short-term cloud is not removed, Obama argued, it could prevent middle class consumers from opening their wallets for holiday gifts, businesses may stop hiring, and the economy could plunge back into a recession.

“We should not hold the middle class hostage while we debate tax cuts for the wealthy,” Obama said. “We should at least do what we agree on, and that’s to keep middle-class taxes low.”

While he said he was still open for compromise, he has previously opposed any efforts to extend tax cuts for families making more than $250,000 a year. He also said that simply limiting tax deductions — a Romney proposal that Obama said he would look at as part of a broad income tax package — is not enough by itself.

But he would not answer directly when asked whether he would not agree to a deal that kept the top tax rate at 35 percent, rather than letting it rise to 39.6 percent.

Obama’s conference served as his outline before he meets with congressional leaders on Friday, their first face-to-face meeting after the election.

House Speaker John A. Boehner expressed optimism that he can cut a deal with Obama, even though they still remain at odds over tax rates for the wealthy.

“There are ways to put revenue on the table without increasing tax rates,’’ Boehner said at a late afternoon press conference, declining to be specific on what types of deductions and loopholes he would eliminate.

Obama also said he had not yet reached out to Romney but hoped to meet with the former Massachusetts governor before the end of the year. Obama revealed little about what he wanted to convey to Romney other than to “have a chance to sit down and talk.”

He praised him for running the 2002 Winter Olympics, saying “that skill set of trying to figure out how . . . we make something work better applies to the federal government.”

Christopher Rowland and Bryan Bender of the Globe staff contributed to this report. Matt Viser can be reached at maviser@globe.com.